This study will examine the intrinsic difficulty of estimating subpopulation characteristics when the identities of the observations are not completely known. Hard clustering and fuzzy clustering techniques are investigated. This study will develop estimation of methodologies for the subpopulation characteristics. The new methodologies will alleviate some of the intrinsic difficulties for a heterogeneous mixture of subpopulations. Applications will be made to study the issues concerning biological heterogeneity and measurement error in the birth weight, gestational age and perinatal mortality. This study will also be applied to the investigation of intrauterine growth and pregnancy outcome.